Thursday, October 14, 2004

Mathematics and psychology meet

Two neurologists discover neurological basis behind the 'Nash Equilibrium,' which is, in the context of a (possibly positive-sum) game of two or more contestants, a collection of strategies whereby no person can alter the strategy and get a better outcome. The fundamental theorem, which extends the theory of the two-person zero-sum game of von Neumann and Morgenstern to any number of contestants and any type of outcome, was part of John Nash's doctoral dissertation in 1949-50 (or so) and earned him the Nobel Prize for Economics in 1994. The advance of this study is that it provides evidence that somehow primate brains (at least those of the primates and humans involved) are somehow 'hard-wired' to discover this equilibrium through repeated play of a single type of game.

I don't know whether the genius and the tragic illness that plagued John Nash had to go hand-in-hand, but I think we should all be thankful for the contributions he made. Maybe his later efforts with the Riemann hypothesis*, had they borne any fruit, might have been more fundamental to pure mathematics, but to have such deep insight into how humans behave (even while quite erratic himself) would still probably be a more important contribution to understanding humans. Thanks, John Nash.